Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
9.1-a1 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 48 a - 123\) , \( 291 a - 749\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(48a-123\right){x}+291a-749$ |
81.1-c1 |
81.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( - 3^{14} \) |
$1.10531$ |
$(3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.828410025$ |
0.414033173 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 435 a - 1115\) , \( -7202 a + 18448\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(435a-1115\right){x}-7202a+18448$ |
144.4-c1 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.59440343$ |
0.775944329 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 117 a - 300\) , \( -876 a + 2244\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(117a-300\right){x}-876a+2244$ |
144.5-c1 |
144.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.5 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.199300429$ |
0.775944329 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -119 a - 186\) , \( -1469 a - 2294\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-119a-186\right){x}-1469a-2294$ |
576.6-e1 |
576.6-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.978485520$ |
$7.242622550$ |
3.437603564 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 100 a - 256\) , \( -813 a + 2081\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(100a-256\right){x}-813a+2081$ |
576.6-n1 |
576.6-n |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.209789527$ |
$18.09797622$ |
1.841701975 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -19 a - 36\) , \( 66 a + 110\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a-36\right){x}+66a+110$ |
576.7-e1 |
576.7-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.978485520$ |
$7.242622550$ |
3.437603564 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -101 a - 157\) , \( -1084 a - 1693\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-101a-157\right){x}-1084a-1693$ |
576.7-n1 |
576.7-n |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.356632445$ |
$2.262247028$ |
1.841701975 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 21 a - 61\) , \( 93 a - 253\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(21a-61\right){x}+93a-253$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.